Abstract
The background, terminology, and theory of a technique (called the Method of Imprecision or MOI) to formally represent and manipulate imprecise information in engineering design calculations is reviewed here [3, 29, 30, 33, 36, 37, 38, 39, 43, 56, 57, 58, 59, 60]. The method utilizes fuzzy sets to capture designers’ and customers’ preferences. Formal methods for including noise, trade-off strategies and design iteration are included.
Two illustrative examples (one of an air tank design, the other the design of a braking system for a passenger vehicle) are presented. The examples emphasize a compareson of different solution alternatives during preliminary engineering design, involving realistic design complexities and decision criteria. Sample numerical and graphical results are given for the applications, including the imprecise input design variables and output performance variables of the design examples. Normalized measures of the importance of, and coupling between, design variables are also presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
AKAO, Y. Quality Function Deployment: Integrating Customer Requirements into Product Design. Productivity Press, Cambridge, 1990.
ALGER, J., AND HAYS, C. Creative Synthesis in Design. Prentice Hall, Englewood Cliffs, 1964.
ANTONSSON, E. K., AND OTTO, K. N. Imprecision in Engineering Design. ASME Journal of Mechanical Design 117(B) (Special Combined Issue of the Transactions of the ASME commemorating the 50th anniversary of the Design Engineering Division of the ASME.) (June 1995), 25–32. Invited paper.
ASIMOW, M. Introduction to Design. Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962.
BELLMAN, R. E., AND GIERTZ, M. On the analytic formalism of the theory of fuzzy sets. Information Sciences 5 (1973), 149–156.
BIEGEL, P., AND PECHT, M. Design trade-offs made easy. Concurrent Engineering 1, 3 (May/June 1991), 29–40.
COLTON, J., AND DESCANIO, J. An integrated, intelligent design environment. Engineering with Computers 7 (1991), 11–22.
Cox, R. T. The Algebra of Probable Inference. Johns-Hopkins University Press, Baltimore, MD, 1961.
DEGROOT, M. H. Optimal Statistical Decisions. McGraw-Hill, New York, 1970.
DLESK, D. C., AND LIEBMAN, J. S. Multiple objective engineering optimization. Engineering Optimization 6, (1983), 161–175.
DONG, W. M., AND WONG, F. S. Fuzzy weighted averages and implementation of the extension principle. Fuzzy Sets and Systems 21, 2 (Feb. 1987), 183–199.
DUBOIS, D., AND PRADE, H. Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York, 1980.
DUBOIS, D., AND PRADE, H. A class of fuzzy measures based on triangular norms. International Journal of General Systems 8 (1982), 43–61.
DUBOIS, D., AND PRADE, H. Criteria aggregation and ranking of alternatives in the framework of fuzzy sets. In TIMS/Studies in the Management Sciences (1984), Elsevier Science Publishers B.V., North-Holland, pp. 209–240.
DUBOIS, D., AND PRADE, H. Possibility Theory: An Approach to the Computerized Processing of Information. Plenum Press, New York, 1988.
ESCHENAUER, H., KOSKI, J., AND OSYCZKA, A., Eds. Multicriteria Design Optimization. Springer-Verlag, Berlin, 1990.
FISHBURN, P. Foundations of Expected Utility. D. Reidel, 1982.
FISHBURN, P. Normative theories of decision making under risk and under uncertainty. In Non-Conventional Preference Relations in Decision Making, J. Kacprzyk and M. Roubens, Eds. Springer-Verlag, New York, 1988, pp. 1–21.
FISHBURN, P.C. Uncertainty aversion and separated effects in decision making under uncertainty. In Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making, J. Kacprzyk and M. Fedrizzi, Eds. Springer-Verlag, New York, 1988. Springer Lecture Notes in Economics and Mathematical Systems, vol. 310.
FRENCH, S. Decision Theory: An Introduction to the Mathematics of Rationality. Ellis Horwood, Chichester, 1988.
GAVIN, JR., J. G. Fly me to the Moon: An interview with Joseph G. Gavin, Jr. Technology Review 97, 5 (July 1994), 61–68.
HALMOS, P. Measure Theory. Springer-Verlag, New York, 1974.
HAUSER, J., AND CLAUSING, D. The house of quality. Harvard Business Review (May/June 1988), 63–73.
HOELTZEL, D. A., AND CHIENG, W.-H. Systems for unified life-cycle mechanical engineering design: Shared-tool architectures versus distributed tool architectures. Engineering with Computers 6, 4 (1990), 211–222.
HOLMES, M. F. Machine dynamics, The need for greater productivity. In Research Needs in Mechanical Systems (New York, 1984), K. N. Reid, Ed., ASME, pp. 140–159.
KACPRZYK, J., AND ROUBENS, M., Eds. Non-Conventional Preference Relations in Decision Making, vol. 301 of Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, New York, 1988.
KEENEY, R., AND RAIFFA, H. Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Cambridge University Press, Cambridge, U.K., 1993.
KRANTZ, D., LUCE, R., SUPPES, P., AND TVERSKY, A. Foundations of Measurement, vol. I. Academic Press, New York, 1971.
LAW, W. S., AND ANTONSSON, E. K. Hierarchical Imprecise Design with Weights. In Proceedings of the Fourth IEEE International Conference on Fuzzy Systems (FUZZ-IEEE/IFES’95) (Mar. 1995), vol. 1, IEEE, pp. 383–388.
LAW, W. S., AND ANTONSSON, E. K. Optimization Methods for Calculating Design Imprecision. In Advances in Design Automation — 1995 (Sept. 1995), vol. 1, ASME, pp. 471–476.
OSYCSKA, A. Multi-Criterion Optimization in Engineering with Fortran Examples. Halstad Press, New York, 1984.
OTTO, K.N. A Formal Representational Theory for Engineering Design. PhD thesis, California Institute of Technology, Pasadena, CA, June 1992.
OTTO, K. N., AND ANTONSSON, E. K. Trade-Off Strategies in Engineering Design. Research in Engineering Design 3, 2 (1991), 87–104.
OTTO, K. N., AND ANTONSSON, E. K. Trade-Off Strategies in the Solution of Imprecise Design Problems. In Fuzzy Engineering toward Human Friendly Systems: Proceedings of the International Fuzzy Engineering Symposium’91, Volume 1 (Yokohama, Japan, Nov. 1991), T. Terano et al., Eds., LIFE, IFES, pp. 422–433.
OTTO, K. N., AND ANTONSSON, E. K. The Method of Imprecision Compared to Utility Theory for Design Selection Problems. In Design Theory and Methodology — DTM’93 (Sept. 1993), ASME, pp. 167–173.
OTTO, K. N., AND ANTONSSON, E. K. Tuning Parameters in Engineering Design. ASME Journal of Mechanical Design 115, 1 (Mar. 1993), 14–19.
OTTO, K. N., AND ANTONSSON, E. K. Design Parameter Selection in the Presence of Noise. Research in Engineering Design 6, 4 (1994), 234–246.
OTTO, K. N., LEWIS, A. D., AND ANTONSSON, E. K. Approximating a-cuts with the Vertex Method. Fuzzy Sets and Systems 55, 1 (Apr. 1993), 43–50.
OTTO, K. N., LEWIS, A. D., AND ANTONSSON, E. K. Determining optimal points of membership with dependent variables. Fuzzy Sets and Systems 60, 1 (Nov. 1993), 19–24.
PAPALAMBROS, P., AND WILDE, D. Principles of Optimal Design. Cambridge University Press, New York, 1988.
PUGH, S. Total Design. Addison-Wesley, New York, 1990.
SANDGREN, E. A multi-objective design tree approach for the optimization of mechanisms. Mechanisms and Machine Theory 25, 3 (1990), 257–272.
SCOTT, M. J., AND ANTONSSON, E. K. Aggregation Functions for Engineering Design Trade-offs. In 9th International Conference on Design Theory and Methodology (Sept. 1995), vol. 2, ASME, pp. 389–396.
SHIGLEY, J. E., AND MITCHELL, L. D. Mechanical Engineering Design, fourth ed. McGraw-Hill Book Company, New York, 1983.
SIDDAL, J. N. Analytical Decision Making in Engineering Design. Prentice-Hall, 1972.
STEUER, R. Multiple Criteria Optimization: Theory, Computation, and Application. J. Wiley, New York, 1986.
SUGENO, M. Theory of fuzzy integrals and its applications. PhD thesis, Tokyo Institute of Technology, 1974.
SUGENO, M. Fuzzy measures and fuzzy integrals — a survey. In Fuzzy Automata and Decision Processes (New York, 1977), M. Gupta et al., Eds., North-Holland, pp. 89–102.
SULLIVAN, L. P. Quality function deployment. Quality Progress (June 1986), 39–50.
SVESHNIKOV, A. Problems in Probability Theory, Mathematical Statistics, and the Theory of Random Functions. Dover Publications, New York, 1968.
TRIBUS, M. Rational Descriptions, Decisions, and Designs. Pergamon Press, New York, 1969.
ULLMAN, D. G. The Mechanical Design Process. McGraw Hill, New York, 1992.
ULRICH, K. T., AND PEARSON, S. A. Does product design really determine 80% of manufacturing cost? Working Paper MSA 3601–93, MIT, Sloan School of Management, Cambridge, MA, Aug. 1993.
WARD, A. C., LIKER, J. K., SOBEK, D. K., AND CRISTIANO, J. J. Set-based concurrent engineering and Toyota. In Design Theory and Methodology — DTM’94 (Sept. 1994), vol. DE68, ASME, pp. 79–90.
WHITNEY, D. E. Manufacturing by design. Harvard Business Review 66, 4 (July 1988), 83–91.
WOOD, K. L., AND ANTONSSON, E. K. Computations with Imprecise Parameters in Engineering Design: Background and Theory. ASME Journal of Mechanisms, Transmissions, and Automation in Design 111, 4 (Dec. 1989), 616–625.
WOOD, K. L., AND ANTONSSON, E. K. Modeling Imprecision and Uncertainty in Preliminary Engineering Design. Mechanism and Machine Theory 25, 3 (Feb. 1990), 305–324. Invited paper.
WOOD, K. L., ANTONSSON, E. K., AND BECK, J. L. Representing Imprecision in Engineering Design — Comparing Fuzzy and Probability Calculus. Research in Engineering Design 1, 3/4 (1990), 187–203.
WOOD, K. L., OTTO, K. N., AND ANTONSSON, E. K. A Formal Method for Representing Uncertainties in Engineering Design. In First International Workshop on Formal Methods in Engineering Design (Fort Collins, Colorado, Jan. 1990), P. Fitzhorn, Ed., Colorado State University, pp. 202–246.
WOOD, K. L., OTTO, K. N., AND ANTONSSON, E. K. Engineering Design Calculations with Fuzzy Parameters. Fuzzy Sets and Systems 52, 1 (Nov. 1992), 1–20.
WOODSON, T. Introduction to Engineering Design. McGraw-Hill, New York, 1966.
YAGER, R. Fuzzy decision making including unequal objectives. Fuzzy Sets and Systems 1 (1978), 87–95.
ZADEH, L. A. Fuzzy sets. Information and Control 8 (1965), 338–353.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Kluwer Academic Publishers
About this chapter
Cite this chapter
Antonsson, E.K., Otto, K.N., Wood, K.L. (1996). Modeling Imprecision in Engineering Design. In: Sebastian, HJ., Antonsson, E.K. (eds) Fuzzy Sets in Engineering Design and Configuration. International Series in Intelligent Technologies, vol 9. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1459-2_1
Download citation
DOI: https://doi.org/10.1007/978-1-4613-1459-2_1
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-8636-3
Online ISBN: 978-1-4613-1459-2
eBook Packages: Springer Book Archive